An Upper Bound for the Mosaic Number of (2,q)-Torus Knots
Jeremy Lamera · John Spoor Broome Library Institutional Repository (California State University) · 2016
In 2014, Hwa Jeong Lee, Kyungpo Hong, Ho Lee, and Seungsang Oh provided and proved an upper bound for the mosaic number of torus knots in their article Mosaic Number of Knots. In this paper, we will provide a new upper bound for the family of (2,q)-torus knots. Rather than approach this from a grid diagram standpoint, such as the proof in Mosaic Number of Knots, we will approach it in the general knot mosaic standpoint by analyzing the structure of an n x n grid. We will determine the mosaic number of (2,q)-torus knots up to the (2,12)-torus knot and establish an upper bound for the family's mosaic number. Additionally, although earlier this year, in February 2016, Ludwig published the article Knot Mosaic Tabulation with a proof for the mosaic number of the 6_3 prime knot, an original though similar proof will be covered as we formulated one independently while searching for the mosaic number of the (2,6)-torus link.